Power and Algebraic Expressions

Power and Algebraic Properties

When we emphasize power we also develop a classroom opportunity to discuss why and how certain algebraic properties work.  For instance, a discussion might evolve regarding whether or not the mathematician can ever stray from the rigid construct of the order of operations.  In fact, we can ‘get around’ the order of operations in some instances by paying attention to the meaning, or value, of a given expression.  If I have 5 + 4 – 3 + 7 how can I manipulate the problem so I don’t have to ‘obey’ the order of operations? I can maintain the value of my expression and express it in all addition: same value, more flexibility in order because the commutative property will now come into play.  5 + 4 – 3 + 7 becomes 5 + 4 + -3 + 7. Now, I can use the commutative property to trump the ‘order’ without changing the value.  I can do this with other expressions as well.  If I have 6 ÷ 2 x 8, I am stuck going from left to right.  But if I can get my expression down to all multiplication, I can use the commutative property of multiplication to re-arrange my order.  So I will re-write this problem as 6 x ½ x 8. Similarly, if I understand the definition of subtraction or the definition of division I can use these definitions (opposites and inverses) to re-write and re-attack my equation. Voila, I am “freed” from the order of operations. Taking advantage of the algebraic properties is a critical emphasis in the CCSS-M, and one that opens up as we consider how we can ‘get around’ the order of operations without changing the value.  Watch this video to think about this even further.